Q. 64.0( 1 Vote )

# A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per second is 1.0 × 10^{19}. Calculate the force exerted by the light beam on the mirror.

Answer :

momentum (p) imparted by 1 photon on the mirror is

Momentum is a vector quantity which has magnitude and direction

So, in below formula we are considering only the component of momentum which is perpendicular to the mirror, note: that the parallel component does not make any contribution, as it is parallel therefore it does not fall any of the area of mirror.

mv is the momentum of light fall but its perpendicular component is mvcosθ and the change in momentum when it reflects is 2 mv cosθ.

p =mv cosθ – (-mv cosθ)

where p= momentum,

m=mass

v= velocity.

p =2mvcosθ

And the momentum of photon is given by its energy (E) speed of light (c). The quantity (mv) in above formula can be written for photon as it is equal to that[momentum of photon is defined to be as its ]. So above formula becomes,

∴ Equation 1

→ 2cosθ. (Rate of change of momentum is force)

→ Force by one photon is

=

∴ Force by photons is =.

=

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